LQG控制的模仿与迁移学习
Imitation and Transfer Learning for LQG Control
AI总结：
本文针对LQG控制，在系统参数未知且多任务场景下，提出基于数据分离原理的模仿与迁移学习方法，可减少约50%的专家数据需求。
摘要：
本文研究线性二次高斯（LQG）控制的模仿与迁移学习设置，其中（i）系统动力学、噪声统计和成本函数未知，并提供专家数据（即最优输入和输出序列）来学习LQG控制器，以及（ii）对同一系统执行多个控制任务，但具有不同的LQG成本。我们证明了可以从长度为$n(l+2)-1$的一组专家轨迹中学习LQG控制器，其中$n$和$l$分别是系统状态和输出的维度。此外，控制器可以分解为估计矩阵（仅依赖于系统动力学）与控制矩阵（依赖于LQG成本）的乘积。这种基于数据的分离原理使我们能够跨不同的LQG任务迁移估计矩阵，并将学习LQG控制器所需的专家轨迹长度减少到$2n+m-1$，其中$m$是输入的维度（对于$l=2$的单输入系统，这大约减少了所需专家数据的$50\%$）。
英文摘要：
In this paper we study an imitation and transfer learning setting for Linear Quadratic Gaussian (LQG) control, where (i) the system dynamics, noise statistics and cost function are unknown and expert data is provided (that is, sequences of optimal inputs and outputs) to learn the LQG controller, and (ii) multiple control tasks are performed for the same system but with different LQG costs. We show that the LQG controller can be learned from a set of expert trajectories of length $n(l+2)-1$, with $n$ and $l$ the dimension of the system state and output, respectively. Further, the controller can be decomposed as the product of an estimation matrix, which depends only on the system dynamics, and a control matrix, which depends on the LQG cost. This data-based separation principle allows us to transfer the estimation matrix across different LQG tasks, and to reduce the length of the expert trajectories needed to learn the LQG controller to~$2n+m-1$ with $m$ the dimension of the inputs (for single-input systems with $l=2$, this yields approximately a $50\%$ reduction of the required expert data).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
